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Motor

Motor Inrush Current

Calculate motor inrush current, voltage drop during startup, and I²t value for fuse/breaker selection.

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Formula

Iinrush=k×IFL,ΔV=Iinrush×RlineI_inrush = k × I_FL, ΔV = I_inrush × R_line
k— Inrush multiplier (5–8 typical) (×)
I²t— Fuse energy rating (A²·s)

How It Works

This calculator determines motor inrush (locked-rotor) current for sizing fuses, circuit breakers, and power supplies. Electrical engineers, panel builders, and industrial electricians use it to ensure protection devices allow motor starting while providing fault protection. Undersized protection trips on every start; oversized protection fails to clear faults, risking equipment damage.

Per NEMA MG-1-12.35 and IEC 60034-12, locked-rotor current (LRC) ranges from 5-8× full-load current for AC induction motors, depending on motor design class. NEMA Design B motors (most common industrial type) specify 6.0-7.0× LRC/FLA ratio. For DC motors, inrush is limited only by armature resistance: I_inrush = V/R_a, which can reach 10-20× running current in the first milliseconds before back-EMF develops.

Inrush duration depends on motor and load inertia. Per IEEE 3002.7, small unloaded motors reach full speed in 50-200 ms. Large loaded motors may take 5-15 seconds, during which current remains elevated. NEC Article 430 specifies motor branch circuit protection: time-delay fuses at 175% FLA or inverse-time breakers at 250% FLA allow transient inrush while providing short-circuit protection. A 10A motor requires a 17.5A time-delay fuse that withstands 60-70A inrush for 0.5-2 seconds.

Worked Example

Size the branch circuit protection for a 7.5 kW, 400V, 50 Hz three-phase induction motor (NEMA Design B). Full-load current is 14.2A per motor nameplate, LRC code letter is G (5.6-6.3× FLA).

Step 1 — Calculate inrush current: Using mid-range LRC ratio of 6.0×: I_inrush = 6.0 × 14.2 = 85.2A peak during starting

Step 2 — Determine inrush duration: Fan load with J = 0.5 kg·m², motor acceleration constant 15 rad/s² Time to full speed: t = ω/α = (1450 × π/30) / 15 = 10.1 seconds Note: Current decays from 85A to 14A over this period, not sustained at peak

Step 3 — Select time-delay fuse per NEC 430.52: For Design B motor: Fuse ≤ 175% of FLA Fuse rating = 1.75 × 14.2 = 24.9A → select 25A time-delay (Type D) Verify: 25A time-delay fuse withstands 85A for ~10s per manufacturer curve

Step 4 — Size supply cable per NEC 430.22: Wire ampacity ≥ 125% × FLA = 1.25 × 14.2 = 17.75A Select 2.5 mm² copper (rated 21A) per IEC 60364

Result: Use 25A time-delay fuse and 2.5 mm² cable. The 85A inrush lasting up to 10 seconds clears without nuisance tripping. The protection still clears a sustained 85A fault (jammed rotor) within the motor's thermal limit of 15 seconds per NEMA MG-1.

Practical Tips

  • ✓Per NEMA MG-1-12.50, limit starting current duration using soft-starters or VFDs for motors >7.5 kW; soft-starters reduce inrush to 2-3× FLA while extending acceleration time to 5-15 seconds
  • ✓Add 1000-4700 µF bulk capacitance per IEC 61000-4-11 guidelines within 100mm of motor driver H-bridge to absorb 10-20A inrush spikes without crashing MCU supply rails
  • ✓For VFD-driven motors, the motor sees zero inrush (gradual V/f ramp), but the VFD input rectifier draws 5-10× inrush from AC mains—size the AC breaker for VFD inrush, not motor inrush

Common Mistakes

  • ✗Using fast-blow (Type gG) fuses for motor circuits: Per IEC 60269-1, fast fuses clear at 2.5× rating in 0.1s—an 85A inrush blows a 25A fast fuse instantly; always specify time-delay (Type gD/aM) for motor protection
  • ✗Sizing DC supply for steady-state current only: Per DC motor physics, inrush reaches V/R_a (10-20× running current); an unregulated supply sags 50% or more without 3-5× current headroom or soft-start circuit
  • ✗Neglecting battery system voltage sag: A 48V battery with 20 mΩ internal resistance drops to 46V during 100A inrush—this 4% sag can reset 3.3V-logic MCUs if their LDO dropout is exceeded

Frequently Asked Questions

Per IEEE 3002.7: Electrical inrush (due to zero back-EMF) decays within 2-5 electrical time constants (L/R), typically 10-50 ms. Mechanical acceleration prolongs elevated current until the rotor reaches operating speed—50-200 ms for small unloaded motors, 5-30 seconds for large loaded machines. The RMS current during acceleration is typically 3-4× FLA due to the decaying profile, even though peak inrush reaches 6-8× FLA.
Per VFD manufacturers (ABB, Siemens): A VFD eliminates motor-side inrush by ramping frequency/voltage over 2-30 seconds. However, the VFD's own DC bus capacitors draw 5-10× rated current from the AC mains during initial power-up. This VFD inrush lasts 50-200 ms and requires appropriately rated AC breakers. Premium VFDs include pre-charge resistors that limit input inrush to 2-3× steady-state current.
Per NEMA MG-1: They describe the same physical phenomenon measured differently. Locked-rotor current (LRC) is the steady-state current with rotor mechanically held at zero speed—used for thermal rating and protection sizing. Inrush current is the transient peak at switch-on, which may exceed LRC by 10-20% for the first half-cycle due to transformer-like DC offset in the magnetic flux. For protection sizing, use LRC; for capacitor sizing and EMC analysis, consider the higher transient peak.

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